A ring S is a central
extension of a subring R if S = RC and C is the centralizer of R in S, i.e.,
C = {s ∈ S;sr = rs} for every r ∈ R. We shall also say that R is centrally embedded
in
We have shown that if a ring R is centrally embedded in a simple artinian ring then
R is a prime Öre ring and its quotient ring Q is the minimal central extension of R
which is a simple artinian ring; furthermore, the centralizer of R can be
characterized. In the present note we extend these results and show that rings which
can be centrally embedded in semi-simple artinian rings are semi-prime Öre rings
with a finite number of minimal primes and their rings of quotients are the minimal
central extension of this type.
